Noise shaping signed digital-to-analog converter

ABSTRACT

A noise-shaping signed digital-to-analog converter is described. A method includes selectively enabling a first sequence of unit elements of a plurality of unit elements of a digital-to-analog converter to convert a signed digital code to a plurality of analog signals in response to a plurality of control signals. Individual control signals of the plurality of control signals and individual analog signals of the plurality of analog signals correspond to respective unit elements of the plurality of unit elements. The method includes generating the plurality of control signals based on a pointer, a magnitude of the signed digital code, and a sign of the signed digital code. The method may include combining the plurality of analog signals with an output of a phase/frequency detector and charge pump in a phase-locked loop. The signed digital code may be an error signal based on a predetermined divide ratio of the phase-locked loop.

BACKGROUND

Field of the Invention

This invention relates to digital-to-analog converters (DACs) and more particularly to use of a DAC to reduce quantization error in a phase-locked loops (PLL).

Description of the Related Art

FIG. 1 illustrates a prior art analog fractional-N PLL where the VCOCLK 101 is a non-integer multiple of the reference clock (REFCLK) 103. The fractional-N divider 107 supplies a feedback signal (DIVOUT) 108 to a phase and frequency detector (PFD) and charge pump 110 that determines the time difference between edges of the REFCLK signal 103 and the feedback signal 108 and supplies a phase error signal based on the time difference to the loop filter 119. The divide value 105, which is supplied to the fractional-N divider 107, is modulated in time to achieve an average divide value corresponding to the desired divide value 109 supplied to the delta sigma (Δ−Σ) modulator logic 111. The delta sigma modulator logic 111 supplies a digital error signal 115 based on the difference between the divide value 105 supplied to the fractional-N divider and the desired divide value 109. The illustrated prior art PLL includes a digital-to-analog converter (DAC) 117 having a current-based output to convert the digital error signal 115 to a current that is added to the charge pump output signal and supplied to the loop filter 119 to reduce quantization noise.

While FIG. 1 shows an analog PLL, digitally controlled oscillators have become common in PLLs. There is a need to achieve high resolution conversion of the phase error between the feedback clock and the reference clock to a digital value. Accordingly, improvements in generating a digital representation of the phase error are desirable.

SUMMARY OF EMBODIMENTS OF THE INVENTION

In at least one embodiment of the invention, a method includes selectively enabling a first sequence of unit elements of a plurality of unit elements of a digital-to-analog converter to convert a signed digital code to a plurality of analog signals in response to a plurality of control signals. Individual control signals of the plurality of control signals and individual analog signals of the plurality of analog signals correspond to respective unit elements of the plurality of unit elements. The method includes generating the plurality of control signals based on a pointer, a magnitude of the signed digital code, and a sign of the signed digital code. The pointer may have a value based on an immediately prior signed digital code. In response to the immediately prior signed digital code being a positive digital code, the value may be an index to a last-used element in a sequence of modularly adjacent used elements of the plurality of unit elements. In response to the immediately prior signed digital code being a negative digital code, the value may be an index to an unused element modularly adjacent to the last-used element. Generating the plurality of control signals may include generating an updated pointer based on the pointer, the magnitude of the signed digital code and the sign of the signed digital code. Generating the updated pointer may include, in response to the sign having a first value, incrementing the pointer based on the magnitude and a modulus. Generating the updated pointer may include, in response to the sign having a second value, decrementing the pointer based on the magnitude and the modulus. The method may include combining the plurality of analog signals with an output of a phase/frequency detector and charge pump in a phase-locked loop. The signed digital code may be an error signal based on a predetermined divide ratio of the phase-locked loop.

In at least one embodiment of the invention, an apparatus includes a digital-to-analog converter circuit. The digital-to-analog converter circuit includes a plurality of unit elements configured to convert a signed digital code to a plurality of analog signals in response to a plurality of control signals. Individual control signals of the plurality of control signals and individual analog signals of the plurality of analog signals correspond to respective unit elements of the plurality of unit elements. The apparatus includes a control circuit configured to generate the plurality of control signals based on a pointer, a magnitude of the signed digital code, and a sign of the signed digital code. The pointer may have a value based on an immediately prior signed digital code. In response to the immediately prior signed digital code being positive, the value may be an index to a last-used element in a sequence of modularly adjacent used elements of the plurality of unit elements. In response to the immediately prior signed digital code being a negative digital code, the value may be an index to an unused element modularly adjacent to the last-used element. The control circuit may include an adder configured to generate an updated pointer based on the pointer, the magnitude of the signed digital code, and the sign of the signed digital code. The apparatus may include a phase-locked loop. The phase-locked loop may include a phase/frequency detector and charge pump, a modulator circuit configured to generate the signed digital code based on a predetermined divide ratio of the phase-locked loop, and a combiner configured to combine the plurality of analog signals with an output of the phase/frequency detector and charge pump.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be better understood, and its numerous objects, features, and advantages made apparent to those skilled in the art by referencing the accompanying drawings.

FIG. 1 illustrates a block diagram of a prior art quantization noise cancelling fractional-N PLL using a current DAC with a traditional phase frequency detector (PFD) and charge pump.

FIG. 2 illustrates a block diagram of a quantization noise cancelling analog fractional-N PLL utilizing a capacitor DAC for cancellation.

FIG. 3 illustrates a block diagram of an embodiment of a quantization noise cancelling digital fractional-N digital PLL utilizing a capacitor DAC, digital nonlinear quantization noise cancellation, and spur cancellation.

FIG. 4A illustrates an embodiment of a capacitor DAC having N unit capacitors, along with a coupling capacitor, and selective precharging capability to a reference voltage or ground, for a resistor based charge pump.

FIG. 4B illustrates a timing diagram associated with the embodiment of FIG. 4A.

FIG. 4C illustrates an embodiment of a capacitor DAC showing a simplified capacitor DAC structure.

FIG. 4D illustrates a timing diagram associated with the embodiment of FIG. 4C.

FIG. 4E illustrates an exemplary output voltage as a function of time for the embodiment of FIG. 4A responsive to a positive digital code input.

FIG. 4F illustrates an exemplary output voltage as a function of time for the embodiment of FIG. 4A responsive to a negative digital code input.

FIG. 4G illustrates exemplary Data Weighted Averaging (DWA) Dynamic Element Matching (DEM) operation of the capacitor DAC of FIG. 4A or 4C.

FIG. 4H illustrates exemplary signed DWA of the embodiment of FIG. 4A or 4C consistent with at least one embodiment of the invention.

FIG. 4I illustrates exemplary control signal generation for the exemplary signed DWA operation of the embodiment of FIG. 4A or 4C consistent with at least one embodiment of the invention.

FIG. 5 illustrates an embodiment of a capacitor DAC using N unit capacitors, along with a coupling capacitor, and selective precharging capability to a reference voltage or ground, for a current source based charge pump.

FIG. 6A illustrates a high level diagram of phase detector logic including generation of timing control signals for the capacitor DAC.

FIG. 6B illustrates a timing diagram associated with the embodiment of FIG. 6A.

FIG. 7A illustrates an embodiment utilizing a frequency divider whose output frequency is four times that of the reference frequency when the PLL is in lock in order to generate enable signals used by the phase detector and capacitor DAC.

FIG. 7B illustrates a timing diagram associated with the embodiment of FIG. 7A.

FIG. 8 illustrates a view of PFD/Charge pump as a Time-to-Voltage Converter (TVC), which, when combined with an analog-to-digital converter (ADC), leads to a Time-To-Digital Converter (TDC) structure.

FIG. 9 illustrates an embodiment of a pseudo-differential TDC which includes two resistor based TVCs, two capacitor DACs for quantization noise cancellation, and two VCO-based ADCs.

FIG. 10 illustrates additional details of the two VCO-based ADCs of FIG. 9.

FIG. 11 illustrates an embodiment of a pseudo-differential TDC which includes two resistor based TVCs, two capacitor DACs for quantization noise cancellation, and two VCO-based ADCs using an input-referred offset consistent with at least one embodiment of the invention.

FIG. 12 illustrates a block diagram of an embodiment of a quantization noise cancelling digital fractional-N digital PLL utilizing a pseudo-differential TDC which includes two resistor based TVCs, two capacitor DACs for quantization noise cancellation, and two VCO-based ADCs using an input-referred offset consistent with at least one embodiment of the invention.

FIG. 13 illustrates the resolution of classical TDC, which is set by an inverter delay.

FIG. 14 illustrates the higher resolution (as compared to the classical TDC) of an embodiment of the TDC described herein in which higher gain in the TVC allows reduction of the impact of the ADC resolution.

FIG. 15A illustrates a raw TDC characteristic assuming a resistor based charge pump in the case where the midpoint charge value occurs when charge(t) has a time span of 2.5 VCO cycles.

FIG. 15B illustrates augmented TDC characteristic in which the usable range of the raw TDC characteristic is extended with the use of a coarse phase detector which adjusts the phase error characteristic to be monotonically increasing across the range of −T/2 to T/2, where T is the reference period.

FIG. 16A illustrates an embodiment of a digital coarse phase detector circuit that determines phase early and phase late signals.

FIG. 16B illustrates a timing diagram associated with the embodiment of FIG. 13A.

FIG. 17 illustrates an embodiment in which the coarse phase detector circuit of FIG. 16A is modified to additionally sense frequency error.

FIGS. 18A and 18B illustrate how the outputs from the digital coarse phase detector and frequency sense circuits are used to augment or adjust the output of the TDC as it is fed into an embodiment of a digital PLL loop filter after being passed through a digital compensation filter.

The use of the same reference symbols in different drawings indicates similar or identical items.

DETAILED DESCRIPTION

Several techniques are described that address wideband PLL phase noise performance. One technique utilizes a capacitor DAC rather than current DAC to achieve ΔΣ quantization noise cancellation. A second technique combines a Time-to-Voltage Converter (TVC) and Voltage-Controlled Oscillator (VCO) based Analog-to-Digital Converter (ADC) to achieve a high performance TDC. Use of a resistor based charge pump in the TVC achieves low flicker noise and avoids current bias circuits, but nonlinearity occurs in the TDC characteristic, which can cause noise folding of the ΔΣ quantization noise. As such, a third technique implements a nonlinear approach to ΔΣ quantization noise cancellation which utilizes the capacitor DAC as well as post ADC (i.e., post TDC) cancellation.

Referring to FIG. 2, rather than using a current DAC as shown in FIG. 1, the PLL 200 uses a capacitor DAC 201 for an analog PLL implementation. The advantages of a capacitor DAC over a current DAC are that it achieves better matching of its elements within a given integrated circuit (IC) area, it requires no static power consumption (i.e., only dynamic power consumption when the capacitors are switched from supply to ground or vice versa), it adds no noise beyond the voltage regulator and switches that provide the voltage reference for the capacitor array elements (i.e., kT/C noise), and it can operate at low supply voltages. In the PLL 200, the phase and frequency detector (PFD) and charge pump 205 supplies a signal corresponding to a time difference between the reference signal ref(t) and the feedback signal div(t) that charges capacitor C₁ while the signal track(t) keeps switch 207 open. Note that given a fixed reference frequency, the phase error is simply a scale factor of the time difference between the reference signal ref(t) and the feedback signal div(t). The capacitor DAC converts the digital error signal associated with the delta sigma modulator 209 to a voltage that is combined with the voltage on C₁. When track(t) closes switch 207, the combined voltage is supplied to control the VCO 211. As with the current DAC approach, proper setting of the gain of the capacitor DAC is required as represented by the digital scale factor 215 (K_(residue)) in FIG. 2. While the value of K_(residue) may be determined using adaptive tuning methods, implementing such tuning methods within an analog PLL typically requires high analog complexity, which can be undesirable for mass production devices since it increases design time and introduces risk to the PLL performance being met across temperature and process variations.

Referring to FIG. 3, instead of using an analog PLL implementation 200, another embodiment utilizes a more digital implementation for PLL 300 when using the capacitor DAC 301. In this case, a high resolution Analog-to-Digital Converter (ADC) 303 digitizes the phase (or time) error signal produced by the PFD/Charge Pump circuits 305. Here the PFD/Charge Pump 305 can be considered as a Time-to-Voltage Converter (TVC) and the combined TVC and ADC 303 can be considered as a Time-to-Digital Converter (TDC) 307. The noise cancellation estimator (Digital ΔΣ Modulator)310 is implemented in a digital manner. Rather than constraining the cancellation to a linear approach, the digital estimator calculates the coefficients of a polynomial p(x) 309 that allows cancellation of the impact of nonlinearity in the TDC circuit 307. A digital compensation filter (Comp. Filter) 311 helps undo the effects of the filtering operation created by switching capacitor C₁ onto capacitor C₂. The use of the capacitor DAC 301 lowers the steady-state range required of the ADC 303 since the variation due to quantization noise is reduced, which also reduces the impact of nonlinearity in the ADC 303. In addition to the analog cancellation offered by the capacitor DAC 301, digital cancellation may also be utilized after the ADC to further reduce noise. In particular, the residual error of the capacitor DAC cancellation is computed as residue₂[k] 314, scaled appropriately, and then subtracted from the phase error signal before it is input to the digital PLL loop filter 315. The use of post ADC cancellation may allow the capacitor DAC 301 to have lower resolution. In fact, the ideal capacitor DAC resolution should be high enough to ensure that its residual error is small enough to reduce or eliminate the impact of nonlinearity in the ADC, but low enough such that the residual error can act as a dithering signal for the ADC to better scramble the impact of its quantization noise. Note that Dynamic Element Matching (DEM) techniques can be applied to the capacitor DAC elements in order to reduce or minimize the influence of capacitor mismatch on the DAC cancellation operation. Finally, the availability of the phase (or time) error signal in the digital domain can be leveraged to achieve fractional and non-fractional spur cancellation as explained further herein.

Capacitor DAC

FIG. 4A illustrates additional details of an embodiment of a capacitor DAC to achieve quantization noise cancellation for a fractional-N PLL and FIG. 4B illustrates timing of control signals associated with the embodiment of FIG. 4A. An array 401 of equal valued unit capacitors, C_(unit), are combined with a coupling cap, C_(c) 402 to adjust the voltage of signal out_(rc)(t). The inclusion of C_(c) 402 allows the C_(unit) capacitors to have large enough size such that desired matching requirements are achieved. Assuming that the sum of the unit capacitors is much greater than C_(c), the value of C₁ is reduced according to C_(c) as indicated in FIG. 4A (C₁-C_(c)) so the capacitance value seen on node 425 is C₁ during charging. The value of C_(c) is chosen large enough to provide the capacitor DAC with adequate range to fully cancel quantization noise caused by dithering of the divider within the fractional-N PLL. The capacitor array is controlled by DAC control logic 404 that receives the signal error[k] corresponding to the quantization noise residue[k] associated with the delta sigma modulator 310 (FIG. 3) that is additionally processed as described further herein to generate error[k]. The DAC control logic 404 converts the error[k] to a value cap_val[k] corresponding to the capacitor control value that corresponds to the error[k] and supplies that control value to the binary-to-thermometer encoder 408. Note that the DAC control logic 404 may also include logic for Dynamic Element Matching (DEM) in order to noise shape the quantization noise due to mismatch of the DAC capacitor elements. The binary-to-thermometer encoder 408 converts the cap_val[k] value to a thermometer code that supplies a bit for each of the unit capacitors in the array to register 406, which in turn supplies the bits to control charging of the unit capacitors through voltage buffers 407.

The embodiment shown in FIG. 4A provides the ability to precharge the unit capacitors. Note that including the coupling capacitor also allows precharging. The ability to precharge the unit capacitors to either V_(dd) or ground on each of their terminals allows 2N+1 DAC levels to be achieved with only N unit capacitors. The DAC control logic 404 receives the dac_pre(t) timing signal that controls when the precharging takes place. As shown in the timing diagram of FIG. 4B, when ch_high(t) is asserted at 420 in synchronism with the dac_pre(t) signal, register 406 is set causing V₀(t) . . . V_(N-1)(t) to precharge to their maximum value while the other side of each unit capacitor is coupled to a regulated supply voltage V_(reg) through switch 403. When the dac_clk(t) signal at 422 clocks in thermometer coded values for the DAC into register 406, V₀(t) . . . V_(N-1)(t) take the value shown at 424, which corresponds to the quantization noise correction voltage that is to be combined with the phase or timing error voltage. Alternatively, the capacitor unit array 401 can be precharged to ground when ch_low(t) is asserted at 426. That causes V₀(t) . . . V_(N-1)(t) to be reset as shown at 428 and the other side of each unit capacitor to be coupled to ground through switch 405. When the dac_clk(t) clocks at 430, V₀(t) . . . V_(N-1)(t) take on the thermometer encoded values clocked into register 406, which corresponds to the quantization noise correction voltage that is to be combined with the phase or timing error voltage.

The capacitor DAC can subtract voltage from the phase error or add voltage to the phase error to correct for the quantization error. When the quantization error is positive and the capacitor DAC needs to subtract voltage from phase error voltage on node 425 to cancel the quantization error, the unit capacitors are precharged to the reference voltage on both terminals before thermometer code in register 406 is updated (at time 433 of FIG. 4F) to determine the quantization error correction. When the quantization error is negative and the capacitor DAC needs to add voltage to out_(rc)(t) (node 425 of FIG. 4A), the unit capacitors are precharged to ground before the thermometer code in register 406 is updated (at time 431 of FIG. 4E) to determine the quantization error correction. The DAC control logic 404 determines whether to precharge to ground or the reference voltage based on the value of the error[k] signal received.

The timing diagram FIG. 4B illustrates the order of switching events for the illustrated embodiment. Discharge(t) signal causes out_(rc)(t) (node 425) to be discharged through switch 415 at the start of the cycle. At the same time, the precharge signal dac_pre(t) is asserted to precharge the capacitor DAC to the reference voltage Vdd or ground before the charge pulse charge(t). The charge pulse, charge(t), then charges out_(rc)(t) according to the phase (or time) error in the PLL. After charging node 425, the capacitor DAC value is updated after the charge pulse is completed by clocking in the thermometer code into register 406, and then the track(t) switch is closed. This timing approach reduces or eliminate having the DAC transient influence the charging characteristic of out_(rc)(t) while the charge(t) switch is closed, and also avoids undesired transient behavior, such as ramping of the out_(rc)(t) node, from being seen by the ADC, since the track(t) switch is only closed after out_(rc)(t) is charged based on the phase error and then altered by the capacitor DAC. High gain is achieved when the ratio of charging current to capacitance is relatively high so that a small change in phase difference causes a relatively large change in out_(rc)(t). The larger the gain, the more noise is suppressed in nodes that follow the out_(rc)(t) node. Having a high gain for phase error relaxes the requirements on the ADC that follows. When the track(t) signal is asserted, switch 417 closes, causing the corrected phase error to be transferred to out_(d)[k]. Then the track(t) signal is de-asserted followed by the discharge(t) signal becoming asserted to start the cycle over again. Overall, the transfer of charge to out_(d)[k] results in the out_(d)[k] voltage being the corrected phase error voltage.

In the embodiment of FIG. 4A the capacitor that is charged by the charge pump may be relatively small. In such case, as described earlier, it is beneficial to use the coupling capacitor 402 between that capacitor and the capacitor DAC in order to allow larger sizes for the capacitor DAC elements (to more easily achieve the desired level of matching of the DAC elements). Also, the coupling capacitor allows precharge/charge operations that double the usable range of the capacitor DAC in terms of the number of levels. However, other embodiments may be able to utilize a simplified capacitor DAC structure. FIG. 4C illustrates an embodiment having a simplified capacitor DAC structure. The embodiment may be suitable for applications in which the capacitor charged by the charge pump is sufficiently large so that the capacitor DAC elements are directly coupled to that capacitor (i.e., no coupling capacitor is required). The timing diagram in FIG. 4D illustrates the order of switching events for the illustrated embodiment.

Referring to FIG. 4A, typical dynamic element matching (DEM) techniques may transform mismatch-induced nonlinearity of voltage buffers 407 and unit capacitors, C_(unit) into noise. However, oversampled systems may use noise-shaping DEM techniques that shape the mismatch noise away from DC to increase the associated signal-to-noise ratio. Techniques for shaping mismatch noise include individual level averaging (ILA), data weighted averaging (DWA), and partitioned DWA. Individual level averaging ensures that the average level for each possible DAC code is a target level. The ILA technique requires additional hardware for tracking data for all codes, which may be cost prohibitive in some applications. Data weighted averaging barrel shifts through the DAC unit elements, starting from the DAC unit element where the previous code left off. Although simple to implement, DWA may cause tones for DC inputs, which is undesirable. Partitioned DWA performs DWA on subsets of the DAC codes and increases circuit complexity.

FIG. 4G illustrates DWA in operation for a 3-bit DAC with eight elements. The mismatch £₁ is the error in producing an analog version of the signed digital code i without any DEM, i.e., the sum of the error in elements 1 through i. The pointer s[k] has a value that is the index to the last element used in a sequence of modularly adjacent used elements for the k-th digital code, such that s[k]=(s[k−1]+code[k])_(modulo N), where N is the number of unit elements in the DAC. When producing the [k]-th output, elements starting at s[k−1]+1 are used, wrapping around if necessary. For example, converting the digital code 5 to an analog signal, when s[k−1]=7, elements 8, 1, 2, 3, and 4 are enabled. Modulo N addition of the value of s[k−1] with the code[k], wraps around from element 8 to element 1 and the pointer s[k] has a value of 4. The mismatch error without DWA, £_(i), will introduce white noise into the analog signal if the input digital code is busy and random. The DACerror [k]=ε_(s[k])−ε_(s[k-1]) and the technique for selecting the unit elements from the plurality of unit elements achieves first-order noise shaping. Note that this conventional DWA technique never repeats selection of a particular unit element until every other unit element in the plurality of unit elements has been used at least once.

Conventional DWA requires that all digital input codes to the DAC are positive numbers and the pointer s[k] always moves in the same direction through the unit elements. In a signed DAC, the same elements can be used to produce either positive or negative outputs and application of DWA, as described above, fails to achieve first-order noise shaping under those circumstances. The partitioned DWA technique may use separate partitions for positive and negative codes, but can cause spurious outputs for certain inputs. In response to inputs that are concentrated near half of the sample rate, such as high-pass shaped noise from a delta-sigma modulator, the input to each partition is near DC, and thus the partitioned DWA technique produces tones, as is characteristic of the DWA technique.

FIG. 4H illustrates a noise-shaping, signed DWA technique. The technique accommodates the signed nature of the DAC architecture when generating the updated pointer s[k] based on signed digital code error[k]. The technique moves the pointer s[k] in a first direction (e.g., forward) in response to a positive code and moves the pointer s[k] in an opposite direction (e.g., backwards) for negative codes. Thus DACerror [k]=£_(s[k]) −ε_(s[k-1]), where s[k]=s[k−1]+code[k] and code[k] is a signed digital code and s[k−1] is the pointer value corresponding to an immediately prior signed digital code. For negative codes, the DAC uses a number of sequential unit elements equal to the magnitude of the code, starting with the unit element indicated by the pointer s[k] and moving backward (e.g., left in FIG. 4F), as opposed to starting with the element having an index after the value of the pointer and moving forward (e.g., right in FIG. 4F). The updated pointer is then positioned to the left of the “last” element used for a negative code, as opposed to at the last element used for a positive code. That is, for a positive digital code, the value of the pointer is the index to the last-used element in the sequence of modularly adjacent used elements of the plurality of unit elements. For a negative digital code, the value of the pointer is the index to the unused element modularly adjacent to the last-used element.

FIG. 4I illustrates operation of exemplary control logic for generating the thermometer coded controls signals that are clocked into the register 406 for the signed DAC using the signed DWA technique. The control signals selectively enable adjacent or modularly adjacent unit elements. The control signals may be stored in the register 406 and provided to voltage buffers 407. In addition to the precharging logic described above, the DAC control 404 includes one or more storage elements and combinational logic that is used to update the pointer s[k]. The error[k] signal is a signed digital code that is added to a prior pointer, i.e., pointer s[k−1], which is generated based on a prior signed digital code, the error[k−1]. The pointer 442 is generated using the prior digital code and has a value of the index of the last unit element used by the prior digital code, which indicates a starting index for a first element used for the signed digital code of error[k]. The updated pointer 444 is generated based on the value stored in pointer 442 and the signed digital code of error[k]. The adder/subtractor (ADD/SUB) 440 uses the sign of the error[k] to determine whether to add or subtract the magnitude of error[k] from the pointer 442 to generate the updated pointer 444. If the sign of error[k] is positive, the adder/subtractor 440 adds the magnitude of the error[k] to pointer 442 to generate the updated pointer 444. The updated pointer 444 has a value of the index to the last-used element of the plurality of unit elements. If the sign of error[k] is negative, the adder/subtractor 440 subtracts the magnitude of the error[k] from the value of pointer 442 to generate the updated pointer 444. The updated pointer 444 has a value indicating the unused element modularly adjacent to the last-used-element. If the addition or subtraction causes an overflow (i.e., the modular computation wraps around), then the adder/subtractor 440 sets the wrap indicator 446. If no overflow occurs (i.e., the modular computation does not wrap around), then the adder/subtractor 440 resets the wrap indicator 446.

The binary-to-thermometer encoder 448 and the binary-to-thermometer encoder 450 convert the pointer 442 and the updated pointer 444, respectively, from binary codes to thermometer codes. Those thermometer codes are exclusive-ored with the wrap indicator 446 to generate the N control signals for the N unit elements of the signed DAC, where M is an integer and N=2^(M) (e.g., M=3 and N=8 or M=6 and N=64). Note that the DAC control 404 and the binary-to-thermometer 408 are exemplary only and other circuits may be used to convert a pointer and a signed digital code into a plurality of control signals for corresponding unit elements of a noise shaping, signed DAC. The N control signals are clocked into register 406 and provided to the N unit elements to generate N analog signals. The resulting N analog signals are then summed, e.g., using compensation capacitor 402, or a summing node only, to generate the analog signal. That analog signal may be combined with the output of phase/frequency detector and charge pump 305 to subtract charge from or add charge to the phase error signal to correct for quantization error in the PLL of FIG. 3.

The noise-shaping, signed DAC technique described above reduces the occurrence of spurs and noise as compared to conventional DAC techniques in response to continuous signed digital codes that are equally likely to include positive and negative digital codes. In response to a change in sign of the continuous signed digital code, the noise-shaping, signed DAC technique repeats selection of at least one unit element that was chosen by the immediately prior non-zero signed digital code. In contrast, conventional DAC techniques never repeat selection of a unit element until every other unit element has been used at least once. The noise-shaping, signed DAC technique requires logic and storage related to only one pointer. In contrast, conventional techniques may require pointer logic and pointer storage for each possible digital code or for each partition of unit elements.

FIG. 5 shows an embodiment in which the capacitor DAC structure is applied when the charge pump is implemented with a current source 501 rather than a resistor 416 as shown in FIG. 4A. FIG. 5 utilizes the same timing shown in FIG. 4B. The advantages of using the resistor based charge pump rather than a current source based charge pump are a lower flicker noise corner and the avoidance of a bias current network to set the charge pump current. The disadvantages of using the resistor based charge pump are a significantly nonlinear charging characteristic when closing the charge(t) switch and the requirement of a low noise voltage regulator to attenuate the impact of supply noise. The nonlinear charging characteristic can be addressed by performing nonlinear quantization noise cancellation. The requirement of a low noise voltage regulator is also shared by the capacitor DAC, and has become common practice for many modern mixed signal designs.

FIGS. 6A, 6B, 7A, and 7B illustrate various aspects of embodiments to realize the various timing signals utilized for phase (or time error) detection and capacitor DAC control. The phase detector and DAC control circuit, shown in FIG. 6A, utilizes enable signals that are generated from the frequency divider output shown in FIG. 7A. In the illustrated embodiment, the frequency divider 701 receives the digitally controlled oscillator (DCO) clock 703 and outputs a signal (div4x(t)) having a frequency that is four times that of the reference clock ref(t) when the PLL is in lock, which simplifies the creation of multiphase enable signals as shown in FIGS. 6A and 6B. By leveraging these enable signals in conjunction with the higher divider frequency, the phase detector logic shown in FIG. 6A is able to achieve the various timing control signals with a relatively simple implementation. Those control signals are utilized, e.g., in the embodiment illustrated in FIG. 4A.

Referring to FIGS. 6A, 6B, 7A, and 7B, when en₀[k] goes high, the phase detector compares the next rising edge of div4x(t) to the reference clock ref(t) rising edge. As shown in FIG. 6A flip-flop 601 receives signal en₀[k]. When en₀[k] goes high, the flip-flop output goes high on the next rising edge of div4x(t). Assuming discharge(t) is 0, causing the other input to AND gate 603 to be high, when the output of flip-flop 601 goes high the output of AND gate 603 goes high causing the charge signal to be asserted. The rising edge of ref(t) causes the charge signal to be deasserted. The logic shown in FIG. 6A is an embodiment to generate the timing signals shown in FIGS. 4B and 6B. The track(t), discharge(t), and dac_pre(t) signals can all be generated using the reference and feedback clocks and the four enable signals. The enable signals en₂[k] and en₃[k] supplied to OR gate 605 ensure that discharge(t) lasts for approximately two div4x(t) cycles. Inverters shown in FIG. 6A, such as inverters 610, are relied upon to create delay in order to achieve non-overlapping regions between the control signals. For example, the precharge signal dac_pre(t) asserts after delay from two inverters and an AND gate after discharge(t) has become asserted. Note that longer inverter chains may be required in practice to achieve sufficiently wide, non-overlap regions that are robust in the face of temperature and process variations.

FIGS. 7A and 7B illustrate an embodiment showing how the frequency divider 701 that supplies div4x(t) may be controlled. As discussed above, the output signal div4x(t) is four times the frequency of the reference clock when the PLL is in lock. The nominal divider value N_(nom)[k] may be, e.g., 60.53, leading to N₀, N₁, N₂, and N₃ nominally having a value of 15. N_(nom)[k] is the sum of N₀-N₃. Note that N₂ is the only value dithered by the digital Δ−Σ modulator in the illustrated embodiment, as illustrated by the dithering shown at 707. The counter 709 provides the select signal to multiplexer 711 to cycle through the four divide values to select N₀-N₃, which are provided to the frequency divider 701. The counter value is also used to generate the enable signals as previously discussed.

High Performance Time-to-Digital Converter

As mentioned earlier, the PD/charge pump circuits can also be viewed as a Time-To-Voltage Converter (TVC) since the time error between the reference clock signal ref(t) and the divider signal div(t) of the PLL is translated to a voltage according to the length of time that the charge(t) switch is closed. Referring to FIG. 8, the illustrated TVC embodiment is a pseudo-differential embodiment that includes a phase detector circuit 801 and a charge pump circuit 802 that provides a positive output (out_(dp)) and a negative output (out_(dm)). By then using the Analog-to-Digital Converter (ADC) 803, which includes ADC 809 and ADC 810, to convert the voltage to a digital value, a Time-to-Digital Converter (TDC) 800 is achieved. A simple Phase Detector (PD) circuit 801 is shown as an example in FIG. 8 that creates a charge(t) pulse which corresponds to the time error between output phases of the reference clock signal and the feedback signal (div(t)) from the divider. Note that the reference clock signal ref(t) edge is assumed to follow the div(t) edge during steady-state operation for the exemplary phase detector circuit 801. Use of the pseudo-differential architecture allows attenuation of unwanted DC common-mode noise signals.

FIG. 9 shows an embodiment of aspects of the pseudo-differential TDC structure 800. The pseudo-differential TDC structure 800 includes two resistor based charge pumps 901 and 903, two capacitor DACs 905 and 907 for quantization noise cancellation, and an analog to digital converter that includes two N-stage voltage controlled oscillator (VCO)-based ADCs 809 and 810. The use of resistor based charge pumps provides the advantage of low 1/f noise, which is often a significant issue in advanced CMOS designs. The resistor based charge pump has better low frequency phase noise performance but also has a non-linear characteristic such that the amount of current supplied is a function of the voltage difference across R₁, which changes in time. Alternatively, current sources could be used in place of the resistor based charge pumps but current sources tend to introduce increased 1/f noise into the system. Once thermal or flicker noise is introduced into the system, it can not be removed. However, the impact of nonlinearities caused by the resistor-based charge pumps can be addressed using signal processing techniques such as nonlinear quantization noise cancellation as previously discussed.

Referring to FIG. 10, the VCOs of ADCs 809 and 810 are implemented as ring oscillators using inverter stages 911 and 915. The frequency of the oscillators is determined by tuning transistors 919 and 917 for inverter stages 911 and tuning transistors 920 and 922 for inverter stages 915. The two resistor based charge pump circuits 901 and 903 charge their outputs in opposite directions according to the charge(t) pulse. The discharge(t) pulse causes the node out_(rcp) 904 to be discharged to ground while the node out_(rcm) 906 charges to a regulated supply voltage Vreg. The output of charge pump circuit 901 feeds directly into NMOS tuning transistors 917 and PMOS tuning transistors 920 to tune the frequency of the VCOs. The output of the charge pump circuit 903 feeds directly into NMOS tuning transistors 922 and PMOS tuning transistors 919 to tune the frequency of the VCOs. The inverter chains 911 and 915 disposed between the tuning transistors and the voltages on the gates of the tuning transistors determine the frequency of the ring oscillators. As shown in FIG. 10, the gate signals of the tuning transistors are supplied by the positive phase error out_(dp)[k] and the negative phase error out_(dm)[k]. The use of both NMOS and PMOS tuning devices in the VCO-based ADC allows a pseudo-differential topology that achieves high tuning gain for controlling the frequency of the ring oscillator within the VCO-based ADC, which provides advantages in noise performance. By utilizing direct voltage tuning of the VCO-based ADCs rather than an approach involving current mirrors, extra current bias circuits are avoided, which yields better noise performance for a given amount of power dissipation, and low voltage operation is readily achieved.

Note that the connections from TVC to VCO-based ADC tuning devices is symmetric in the sense that out_(dp)[k] and out_(dm)[k] each influence both NMOS and PMOS devices, which improves even order cancellation of nonlinearity in the ADCs and also helps to reduce the impact of gate leakage on these nodes. However, this connection arrangement largely removes information of the common-mode value of out_(dp)[k] and out_(dm)[k] from the ADC outputs. Fortunately, the common-mode value of out_(dp)[k] and out_(dm)[k] is implicitly set by the opposite charging characteristics of the TVC outputs, and the capacitor DAC input values can be set to have opposite sign as shown in FIG. 10. Since this arrangement leads to a common-value of zero from the pseudo-differential capacitor DACs, undesired common-mode variations of out_(dp)[k] and out_(dm)[k] due to mismatch will not be suppressed. Fortunately, the impact of such mismatch-induced common-mode variations are insignificant assuming design practices are employed to ensure matching between the circuit elements of the TDC, and appropriate calibration techniques are employed. As FIGS. 9 and 10 imply, the use of a VCO-based ADC rather than an alternative ADC structure offers a relatively simple implementation of the overall TDC. FIG. 10 also shows transition counter logic 925, which determines the number of edges that occur in the oscillator of the VCO-based ADC within a given measurement interval and thus provides an indication of frequency of the respective oscillator.

As a representative example of operation, note that phase error leading to an increased pulse width for the charge(t) signal will cause node out_(dp)[k] to increase in voltage and the node out_(dm)[k] to decrease in voltage for the circuit shown in FIG. 10. In turn, the higher voltage of node out_(dp)[k] and lower voltage of node out_(dm)[k] will lead to an increase in the frequency of the ring oscillator 911 in ADC 809 and a decrease in the frequency of ring oscillator 915 in ADC block 810. The resulting change in frequency is due to the fact that higher voltage on the gates of the NMOS transistors 917 and lower voltage on the gates of the PMOS transistors 919 leads to increased current availability for inverter stages 911 and therefore a higher frequency of oscillation. Similarly, a lower voltage on the gates of the NMOS transistors 922 and higher voltage on the gates of the PMOS transistors 920 leads to decreased current availability for inverter stages 915 and therefore a lower frequency of oscillation. For the case of phase error leading to a decreased pulse width for the charge(t) signal, node out_(dp)[k] will decrease in voltage and node out_(dm)[k] will increase in voltage leading to a decrease in the frequency of the ring oscillator 911 in ADC 809 and an increase in the frequency of ring oscillator 915 in ADC block 810. Therefore, subtraction of the measured frequency values of VCO-based ADC blocks 809 and 810 leads to an error signal proportional to the phase error. The outputs of transition counters 925 provide an indication of the VCO-based ADC frequency information as digital signals. Therefore, as shown in FIG. 10, the positive out_(tdcp)[k] signal and the negative out_(tdcm)[k] signal are subtracted in summer 805 to generate the out_(tdc)[k] signal that is a digital value that corresponds to the phase error. Note that in FIG. 10, both voltages are used to tune oscillators 911 and 915. In other embodiments, the voltage out_(dp)[k] may be used alone to tune oscillator 911 and out_(dm)[k] may be used alone to tune oscillator 915. Alternatively, tuning transistors 919 and 920 (or 917 and 922) could be omitted entirely. Note that the voltage controlled oscillators used in various embodiments shown, e.g., in FIGS. 9 and 10, may also be implemented by using an intermediate circuit to convert the voltage of the TVC into one or more currents, and then supplying the current(s) to control the frequency of one or more current controlled oscillators.

To obtain the benefits of using a pseudo-differential architecture, ADC 809 and ADC 810 should operate independently, although the VCOs (the ring oscillator 911 and the ring oscillator 915, respectively) of the ADC 809 and the ADC 810 oscillate within the same frequency range. Each of the VCOs draws an oscillation current, I_(OSC), and a current may be injected from one of the VCOs to the other VCO. For small, non-zero, differential inputs, that injection current may cause one of the VCOs to injection lock to the other VCO. That is, one of the VCOs couples to the other VCO and the VCOs oscillate at the same frequency. In general, injection locking and injection pulling are frequency effects that can occur when a harmonic oscillator is disturbed by a second oscillator operating at a nearby frequency. The injection locking range is approximately

${f_{L} \approx {\frac{f_{osc}}{2Q} \times \frac{I_{inj}}{I_{osc}}}},$

where f_(osc) is approximately the center frequency of each VCO, Q is the quality factor of the VCO, I_(inj) is the magnitude of the current injected from one VCO to another, and I_(osc) is the current drawn by each VCO. As a result of the injection locking, operation of the VCO-based ADC of pseudo-differential TDC 800 includes a dead band at the VCO-based ADC input, i.e., pseudo-differential TDC 800 cannot distinguish between small inputs and a zero input level, which can be catastrophic in some applications. When the VCO-based ADC has an input-referred offset, the dead band is not centered around the zero input level, but rather, is centered around the input-referred offset level of the VCO-based ADC and pseudo-differential TDC 800 may not be able to distinguish between inputs with a small variation from the input-referred offset level and the input-referred offset level.

A technique for reducing or eliminating effects of a dead band caused by injection locking in a VCO-based ADC includes reducing the injection current by physically separating the layouts of the VCOs (e.g., the ring oscillator 911 and the ring oscillator 915) on an integrated circuit substrate to intentionally separate injection current paths. However, physical separation on an integrated circuit substrate to reduce the injection current may not improve the quality factor of those VCOs since physical separation may increase device mismatch. In addition, the physical separation of the VCOs may increase the area and cost of the integrated circuit. Circuit techniques for reducing or eliminating effects of a dead band caused by injection locking in a VCO-based ADC include utilizing voltage regulator designs that increase power supply rejection to reduce the injection current. Those circuit design techniques may substantially increase area and cost of the integrated circuit. In addition, note that these physical design techniques and circuit design techniques may reduce coupling between the two VCO-based ADCs to mitigate, but not eliminate injection locking.

Referring to FIG. 11, a feedback technique that eliminates injection locking in in a VCO-based ADC shifts the frequency ranges of the two VCOs away from each other. Since the VCO-based ADC is configured in a negative feedback loop (e.g., PLL 300 of FIG. 3) including at least one integrator after the VCO-based ADC, the negative feedback loop maintains the output of the VCO-based ADC at zero mean. Accordingly, digital application of a predetermined digital code at the output of the VCO-based ADC causes an offset at the input of the VCO-based ADC that effectively shifts the frequency ranges of the two VCOs away from each other to eliminate injection locking. FIG. 11 illustrates application of a digital offset code os at the output of the VCO-based ADC to induce an input-referred offset that shifts the frequency ranges of the two VCOs away from each other. If the input-referred offset is greater than half the ADC input range, then the frequency ranges of the two VCOs become mutually exclusive, and injection locking is no longer possible. However, that input-referred offset must be tolerated by the other elements of the feedback loop. The input-referred offset technique for eliminating injection locking in a VCO-based ADC may be applied to any system where feedback drives the VCO-based ADC input to zero on average.

In at least one embodiment, the ADC frequency offset 1204 stores one or more digital values that the combiner 1206 combines with the output of the VCO-based ADC. For example, summing node 1202 combines the digital offset code os with a single-ended output signal of the VCO-based ADC 803. However, combiner 1206 may digitally apply the digital offset code to the negative feedback loop using other equivalent combination operations and may be performed using one or more digital offset codes provided by ADC frequency offset 1204 (e.g., combination of the digital offset code os with out_(tdcp)[k] prior to summing node 1208, combination of the digital offset code with out_(tdcm)[k] prior to summing node 1208, or combination of a first digital offset code osp with out_(tdcp)[k] and a second digital offset code osm with out_(tdcm)[k] prior to summing node 1208).

Referring to FIG. 12, in at least one embodiment, the PLL 1200, combines a digital offset code with a digital signal based on an output of the ADC 303. That combination may be performed in other locations of the forward path of the PLL 1200. For example, the combiner 1202 may be included in the compensation filter 311, or included before, after, or within the digital loop filter 315 to combine a suitable digital offset code stored in the ADC frequency offset 1204 with other versions of the digital signal in the forward path, prior to the DCO 317. Rather than introducing the digital offset at the output of the VCO-based ADC, as described above, intentionally mismatching the VCO-based ADC circuits by an amount that offsets the VCO frequency ranges, however, such implementation also reduces efficacy of the pseudo-differential design due to the lack of matching between the complementary sides.

The digital offset code has a predetermined value that is sufficient to cause the VCO-based ADC circuits to oscillate with nonoverlapping frequencies ranges. The digital offset code may be determined empirically during production test or during initialization by characterization of an associated integrated circuit and may be stored in non-volatile memory for later use in a target application. The digital offset code may be updated dynamically during operation of the associated integrated circuit, although such updates may not be necessary in some applications.

A particular advantage of the combined TVC and VCO-based ADC structure for realizing a TDC is that the impact of the ADC quantization noise (and ADC thermal and flicker noise) can be reduced by increasing the gain in the TVC. As indicated in FIGS. 13 and 14, the ability to reduce the impact of quantization noise is in contrast to classical TDC designs in which the quantization noise is set by the inverter delay in the CMOS process being used. FIGS. 13 and 14 show a comparison of resolution of the classical TDC (FIG. 13), which is set by an inverter delay, versus the TDC described herein (FIG. 11), in which higher gain in the TVC allows reduction of the impact of the ADC resolution. In FIG. 13 the rising edge of Ref clock determines the falling edge of the Enable signal. When ref clock rises at 1101, the enable signal falls at 1103 and the count stops at 1105. If the ref signal rises later at 1107 because of a larger phase difference the enable signal continues until 1109 and the count continues until 1111. However, the count value in FIG. 13 has a constant slope such that resolution can be increased only by reducing inverter delay in the TDC. In FIG. 14, the enable signal, which corresponds to the charge(t) signal, similarly takes on a pulse width corresponding to the difference in time between the rising edges of the divider output (DIV) and ref clock. However, the count value in FIG. 14 (1120 or 1122) is determined by the pulse width of the enable signal in combination with the gain of the TVC and the delay per stage of the VCO-based ADC. A large gain in the TVC ensures that the count value produced by the ADC over the measurement interval T_(measure), which typically corresponds to the period of the ref clock, will be significantly impacted by the phase error change reflected in the voltage error signal supplied to the ADC. In particular, a large TVC gain will lead to a wider range of frequency variation in the VCO-based ADC for a given range of phase error, and therefore lead to a higher range of count values for that given range in phase error such that each change in count value corresponds to a smaller phase error step size. The different count values for different phase errors are reflected in the count values 1120 and 1122.

Larger gain in the TVC shown in FIG. 10 is achieved by reducing the value of R₁C₁ such that nodes out_(rcp)(t) and out_(rcm)(t) have a faster charging characteristic as a function of the charge(t) pulse width. In an exemplary embodiment the resistance R₁ is 1 kOhms, the capacitance C₁ is approximately 350 fF, the coupling capacitor C_(c) is approximately ⅓ to ½ of C₁ and the unit capacitors (see FIG. 4A) are approximately 50 fF. These particular values are only examples and the capacitor values used in any particular embodiment can change based on the requirements of the particular embodiment and process technology. While a faster charging characteristic can provide increased gain, increased TVC gain leads to a smaller phase error detection range and higher nonlinearity seen by the divider-induced quantization noise. As such, design of the TVC gain value involves a tradeoff between lowering the impact of noise in the VCO-based ADC versus achieving adequate phase detector range to accommodate noise and perturbations in the PLL phase error signal and reasonable levels of nonlinearity to achieve the desired level of performance of the nonlinear quantization noise cancellation.

The PLL generally requires a wider phase detection region to acquire frequency lock than during steady-state operation, which only requires an adequately large phase detection range to accommodate noise and perturbations. Some embodiments may augment the raw TDC characteristic with a coarse phase detector that is only active outside of the steady-state operating range of the phase (or time) error signal. FIG. 15A illustrates the raw TDC characteristic at 1201 assuming the resistor based charge pump in the case where the midpoint charge value occurs when charge(t) has a time span of 2.5 DCO cycles. That nominal time span is assumed to provide an adequate cushion of time for maintaining a reasonably large minimum pulse width for charge(t) given the expected changes due to change in the divider value of approximately ±one DCO cycle that occurs when using a 2^(nd) order delta-sigma modulator to control the frequency divider. When the nominal time span of charge(t) is set to be longer than 2.5 DCO cycles through appropriate choice of R₁C₁ in FIG. 10 (or I/C₁ for a current based charge pump), the nonlinearity experienced by the Δ−Σ quantization noise will be reduced but the TVC gain will also be reduced. The nominal charging value is set to approximately half the value of V_(reg) (the regulated supply voltage used to charge the capacitors based on the charge(t) signal).

Because of the narrow range of particular embodiments of the TDC structure, an augmented detection scheme may be desirable in order to reliably achieve lock conditions for the PLL. In other embodiments, the coarse phase detector may not be needed given a monotonic characteristic of the TDC. FIG. 15B illustrates how the augmentation works in one embodiment such that a monotonically increasing error curve is achieved across the time error range of −T/2 to T/2 with the coarse phase detector output being added to the TDC output in the digital domain. If the PLL is determined to be in a phase early condition (time errors Δt less than zero), the coarse phase detector output is assumed to be negative such that the TDC output is reduced as indicated at 1203. If the PLL is determined to be in a phase late condition (time errors Δt greater than the steady-state operating range of the TDC such as Δt greater than T/4), the coarse phase detector output is assumed to be positive such that the TDC output is increased as indicated at 1205. The relative scale factors of the coarse phase detector outputs in relation to the TDC output is set such that a monotonically increasing (or decreasing for some embodiments) error characteristic is achieved from their combined output and proper settling behavior is achieved for the PLL. In the illustrated embodiment, the period (T) of the ref clock is divided into quartiles to determine when phase early and phase late occur. The quartile 1207 between 0 and T/4 is assumed to be the steady-state operating range of the TDC.

FIG. 16A illustrates an embodiment of a digital coarse phase detector circuit that determines phase early and phase late. FIG. 16B illustrates a timing diagram associated with the circuit of FIG. 16A. Referring to FIG. 16B, en₀[k], en₁[k], en₂[k], and en₃[k] correspond to the four phases of the div4x(t) divide signal. As described above, the div4x(t) corresponds to a feedback signal having a frequency that is four times that of the reference signal when the PLL is in lock. FIG. 16B illustrates the timing associated with the phase ok region 1321 corresponding to region 1207 (see FIG. 15B). The digital coarse phase detector circuit of FIG. 16A determines if the phase region is phase late in 1323 or phase early in 1325. Note that the digital coarse phase detector circuit of FIG. 16A is intrinsically active (provides an asserted ph_(early)[k] or ph_(late)[k] signal) only when the PLL is out of lock. FIG. 17 illustrates another embodiment in which the coarse phase detector circuit of FIG. 16A is modified to include a digital counter 1401 and digital Δ count logic 1403 to sense frequency error. When the PLL is locked there will be four div4x cycles per ref clk cycle. Greater than four div4x cycles implies that the DCO frequency is too high such that freq_(hi)[k] is asserted. Less than four div4x cycles implies that the DCO frequency is too low such that freq_(lo)[k] is asserted.

FIGS. 18A an 18B illustrate one embodiment of how the outputs from the digital coarse phase detect and frequency sense circuits are used in the loop filter to augment or adjust the output of the TDC that is supplied to the loop filter after it has been passed through a digital compensation filter. FIG. 18A shows the loop filter input in_(LF)[k] adjusted in summer 1501 by a signal based on gain K_(PD) and the ph_(late)[k] and ph_(early)[k] signals. In general, K_(PD) is chosen in order achieve a monotonically increasing (or decreasing) phase error characteristic in the range of −T/2 to T/2 as shown in FIG. 18B. The adjusted signal is supplied from summer 1501 to the digital low pass filter 1502. In addition, the augmented signal is supplied to the summer 1503, where it is added to a signal based on gain K_(FD) and the freq_(hi)[k] and freq_(lo)[k] signals (see FIG. 17). FIG. 18 illustrates that summer 1503 supplies its output to digital accumulator 1505, which is summed with the low pass filter output to generate the overall loop filter output out_(LF)[k].

Additional techniques for improving performance of the phase-locked loop of FIG. 3 (e.g., techniques for generating and using frequency_error[k] and coarse_phase_error[k], quantization noise cancellation 317, and spur cancellation 319) are described in U.S. patent application Ser. No. 14/448,482, filed Jul. 31, 2014, entitled “Time-to-Digital Converter Based on a Voltage Controlled Oscillator,” naming Michael H. Perrott as inventor, now U.S. Pat. No. 9,270,288, issued on Feb. 23, 2016, which application is incorporated herein by reference.

The description of the invention set forth herein is illustrative, and is not intended to limit the scope of the invention as set forth in the following claims. For example, while the noise-shaping, signed DAC technique has been described herein with a particular number and type of unit elements, one of skill in the art will appreciate that the teachings herein can be utilized with other numbers and types of unit elements. In addition, while the noise-shaping, signed DAC technique has been described herein for use in a PLL application, one of skill in the art will appreciate that the teachings herein can be utilized in other applications. Variations and modifications of the embodiments disclosed herein, may be made based on the description set forth herein, without departing from the scope of the invention as set forth in the following claims. 

What is claimed is:
 1. A method comprising: selectively enabling a first sequence of unit elements of a plurality of unit elements of a digital-to-analog converter to convert a signed digital code to a plurality of analog signals in response to a plurality of control signals, individual control signals of the plurality of control signals and individual analog signals of the plurality of analog signals corresponding to respective unit elements of the plurality of unit elements; and generating the plurality of control signals based on a pointer, a magnitude of the signed digital code, and a sign of the signed digital code, wherein the pointer has a value based on an immediately prior signed digital code, wherein in response to the immediately prior signed digital code being a positive digital code, the value is an index to a last-used element in a sequence of modularly adjacent used elements of the plurality of unit elements, and wherein in response to the immediately prior signed digital code being a negative digital code, the value is an index to an unused element modularly adjacent to the last-used element.
 2. The method, as recited in claim 1, wherein the generating the plurality of control signals comprises: generating an updated pointer based on the pointer, the magnitude of the signed digital code and the sign of the signed digital code.
 3. The method, as recited in claim 2, further comprising: storing the updated pointer as the pointer for a next signed digital code.
 4. The method, as recited in claim 1, further comprising: combining the plurality of analog signals to generate an analog signal corresponding to the signed digital code.
 5. The method, as recited in claim 1, further comprising: combining the plurality of analog signals with an output of a phase/frequency detector and charge pump in a phase-locked loop, wherein the signed digital code is an error signal based on a predetermined divide ratio of the phase-locked loop.
 6. The method, as recited in claim 1, wherein in response to the signed digital code and an immediately prior signed digital code both being non-zero and having opposite signs, the first sequence of unit elements includes at least one enabled unit element that was also enabled by the immediately prior signed digital code.
 7. A method comprising: selectively enabling a first sequence of unit elements of a plurality of unit elements of a digital-to-analog converter to convert a signed digital code to a plurality of analog signals in response to a plurality of control signals, individual control signals of the plurality of control signals and individual analog signals of the plurality of analog signals corresponding to respective unit elements of the plurality of unit elements; and generating the plurality of control signals based on a pointer, a magnitude of the signed digital code, and a sign of the signed digital code, wherein the generating the plurality of control signals comprises generating an updated pointer based on the pointer, the magnitude of the signed digital code and the sign of the signed digital code, wherein generating the updated pointer comprises: in response to the sign having a first value, incrementing the pointer based on the magnitude and a modulus; and in response to the sign having a second value, decrementing the pointer based on the magnitude and the modulus.
 8. The method, as recited in claim 7, wherein the generating the updated pointer further comprises: adding the signed digital code and the updated pointer, the signed digital code having M bits and the updated pointer having M bits, where M is an integer greater than zero; and setting a wrap signal in response to an overflow generated by the incrementing or decrementing.
 9. The method, as recited in claim 8, wherein the generating the plurality of control signals further comprises: converting the pointer to a first thermometer-coded signal; converting the updated pointer to a second thermometer-coded signal; and performing an exclusive-OR of the first thermometer-coded signal, the second thermometer-coded signal, and the wrap signal to generate the plurality of control signals.
 10. The method, as recited in claim 7, wherein in response to the signed digital code and an immediately prior signed digital code both being non-zero and having opposite signs, the first sequence of unit elements includes at least one enabled unit element that was also enabled by the immediately prior signed digital code.
 11. The method, as recited in claim 7, further comprising: combining the plurality of analog signals with an output of a phase/frequency detector and charge pump in a phase-locked loop, wherein the signed digital code is an error signal based on a predetermined divide ratio of the phase-locked loop.
 12. An apparatus comprising: a digital-to-analog converter circuit comprising a plurality of unit elements configured to convert a signed digital code to a plurality of analog signals in response to a plurality of control signals, individual control signals of the plurality of control signals and individual analog signals of the plurality of analog signals corresponding to respective unit elements of the plurality of unit elements; and a control circuit configured to generate the plurality of control signals based on a pointer, a magnitude of the signed digital code, and a sign of the signed digital code, wherein the pointer has a value based on an immediately prior signed digital code, wherein in response to the immediately prior signed digital code being a positive digital code, the value is an index to a last-used element in a sequence of modularly adjacent used elements of the plurality of unit elements, and wherein in response to the immediately prior signed digital code being a negative digital code, the value is an index to an unused element modularly adjacent to the last-used element.
 13. The apparatus, as recited in claim 12, wherein the control circuit comprises: an adder configured to generate an updated pointer based on the pointer, the magnitude of the signed digital code, and the sign of the signed digital code.
 14. The apparatus, as recited in claim 13, wherein the adder is configured to increment the pointer based on the magnitude and a modulus, and wherein the adder is configured to decrement the pointer based on the magnitude and the modulus.
 15. The apparatus, as recited in claim 13, wherein the control circuit comprises: a first storage element configured to store the pointer; and a second storage element configured to store the updated pointer; and a third storage element configured to store a wrap indicator having a value indicative of an overflow generated by the adder.
 16. The apparatus, as recited in claim 12, wherein the control circuit comprises: a first binary-to-thermometer encoder responsive to the pointer; a second binary-to-thermometer encoder responsive to an updated pointer; and an exclusive-or configured to generate the plurality of control signals based on an output of the first binary-to-thermometer encoder, an output of the second binary-to-thermometer encoder, and a wrap indicator.
 17. The apparatus, as recited in claim 12, further comprising: a summing node configured to combine the plurality of analog signals to generate an analog signal corresponding to the signed digital code.
 18. The apparatus, as recited in claim 12, further comprising: a phase-locked loop comprising: a phase/frequency detector and charge pump; a modulator circuit configured to generate the signed digital code based on a predetermined divide ratio of the phase-locked loop; and a combiner configured to combine the plurality of analog signals with an output of the phase/frequency detector and charge pump.
 19. The apparatus, as recited in claim 12, wherein in response to the signed digital code and an immediately prior signed digital code both being non-zero and having opposite signs, the plurality of control signals being configured to enable at least one unit element of the plurality of unit elements that was also enabled by the immediately prior signed digital code. 